Question: Mustafa is flying his kite, and Ana is watching. From Ana's perspective there is an angle of $109^\circ$ between Mustafa and his kite. From Mustafa's perspective, there is an angle of $47^\circ$ between Ana and the kite. If the length of the string between Mustafa and the kite is $46 \,\text{m}$, how far is Ana from the kite? Do not round during your calculations. Round your final answer to the nearest meter.
Explanation: Converting the problem into geometrical terms Our problem can be modeled by the following triangle $\triangle ABC$, where we want to find $AC=d$. $A$ $B$ $C$ $109^\circ$ $47^\circ$ $46\text{ m}$ $d$ Since we are given one side length and two angle measures, we can use the law of sines. Using the law of sines $\begin{aligned} \dfrac{\sin(A)}{BC}&=\dfrac{\sin(B)}{AC} \\\\ \dfrac{\sin(109^\circ)}{46} &= \dfrac{\sin(47^\circ)}{d} \gray{\text{Substitute}} \\\\ d \cdot \sin(109^\circ) &= 46 \cdot \sin(47^\circ) \\\\ d &= \dfrac{46 \cdot \sin(47^\circ) }{\sin(109^\circ) } \\\\ d &\approx 36 \,\text{m} \end{aligned}$ The answer Ana is $36$ meters from the kite.